Transcript 9-2 Sample Proportions

Daniel S. Yates
The Practice of Statistics
Third Edition
Chapter 9:
Sampling Distributions
Copyright © 2008 by W. H. Freeman & Company
Sample Proportions
To estimate the proportion of successes in the population:
Take an SRS from the population of interest.
phat = count of successes in the sample/size of sample = X/n
•Note that X and phat are random variables
•If the population is much larger than the sample, X is
distributed binomially
The mean and standard deviation for the sampling
distribution of a sample proportion are algebraically
derived from what we already know about the mean and
standard deviation of a binomial random variable.
Note: phat is less variable in larger samples.
Rule of Thumb 1 will be used throughout the course
whenever we draw a sample to make an inference about a
population.
Remember we only sample when a population is large
enough to make a census impractical.
This rule should sound familiar. We used it when
calculating binomial probabilities with the Normal
approximation.
Note:
The accuracy of the Normal approximation improves as
n increases.
For a fixed sample size, the normal approximation is
most accurate when p is close to .5.
Applying to College
• SRS of 1500 1st year college students on
whether they applied for admission to any
other college. 35% applies to other colleges
besides the one they were attending.
• What is the probability that a random
sample of 1500 students will give a result
within 2 percentage points of this true
value?
• Note that these calculations are virtually the
same as those done in chapter 2. But now
we know the proportion of the area under
the Normal curve is the same as the
probability. 